BOSTON  — The rising cost of higher education is dogging Americans into retirement, with people aged 65 and older still carrying some $18.2 billion in unpaid student loans, according to a federal report released on Wednesday.

While the Government Accountability Office report noted that relatively few U.S. households headed by people 65 or over are carrying student loans, the value of the unpaid debt had spiked from $2.8 billion in 2005, before the financial crisis.

That debt is concentrated in a small number of homes. Just 4 percent of households headed by someone 65 or older carried student loan debt as of 2010, up from 1 percent in 2004.

“Some may think of student loan debt as a just a young person’s problem,” said Senator Bill Nelson, who heads a Senate committee on aging and held a hearing on the findings on Wednesday. “As it turns out, that’s increasingly not the case.”

The $18.2 billion figure includes loans related to both the holders’ education, often for those who have returned to school later in life, and their children’s education, the report found.

Across the United States, about 40 million Americans are paying back some $1.1 trillion in student loan debt.

Student loans are a particular concern, because unlike credit card debt or mortgages, they are typically government-backed and cannot be written off in bankruptcy proceedings, leaving retirees facing the risk of having their Social Security payments garnished to cover student loans.

The cost of higher education in the United States has steadily increased over the past decade, with one year’s costs for tuition, room and board, and other fees at the average four-year U.S. college coming to $23,872 for the 2012-2013 academic year, according to Department of Education data. That is up 21 percent, accounting for inflation.